Excursions of diffusion processes and continued fractions

Details Excursions of diffusion processes and continued fractions Excursions of diffusion processes and continued fractions

2009-06-25

arxiv.org/abs/0906.4651v2

Mathematics

Probability

28 pages. Minor changes to Section 5

Scientific paper

It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.

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